Q. Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio
A) 16 : 1
B) 4 : 1
C) 2 : 1
D) 1 : 1
Explanation
(a) Energy density = $\frac{1}{2}\ stress \times strain$
= $\frac{1}{2}stress \times \frac{stress}{Y} = \frac{(stress)^{2}}{2Y} \propto \frac{1}{D^{4}}\ $
Now , $\frac{u_{A}}{u_{B}} = \frac{D_{B}^{4}}{D_{A}^{4}} = (2)^{4} = 16$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.